Properties

Level $15$
Weight $0$
Character 15.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 4.22329657414 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.328577148\) \(a_{3}=-0.577350269\) \(a_{4}=+0.765117238\) \(a_{5}=+0.447213596\)
\(a_{6}=+0.767054374\) \(a_{7}=-0.907874574\) \(a_{8}=+0.312059870\) \(a_{9}=+0.333333333\) \(a_{10}=-0.594157763\)
\(a_{11}=+1.550840213\) \(a_{12}=-0.441740643\) \(a_{13}=+0.004455899\) \(a_{14}=+1.206181412\) \(a_{15}=-0.258198890\)
\(a_{16}=-1.179712850\) \(a_{17}=-0.295148470\) \(a_{18}=-0.442859049\) \(a_{19}=+1.474943041\) \(a_{20}=+0.342170831\)
\(a_{21}=+0.524161630\) \(a_{22}=-2.060410868\) \(a_{23}=+0.194468611\) \(a_{24}=-0.180167850\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.005920006\) \(a_{27}=-0.192450090\) \(a_{28}=-0.694630487\) \(a_{29}=+1.794951311\) \(a_{30}=+0.343037145\)
\(a_{31}=+0.127670631\) \(a_{32}=+1.255279664\) \(a_{33}=-0.895378015\) \(a_{34}=+0.392127513\) \(a_{35}=-0.406013852\)
\(a_{36}=+0.255039079\) \(a_{37}=-0.272248336\) \(a_{38}=-1.959575619\) \(a_{39}=-0.002572615\) \(a_{40}=+0.139557416\)
\(a_{41}=-1.815521962\) \(a_{42}=-0.696389163\) \(a_{43}=+1.297928456\) \(a_{44}=+1.186574581\) \(a_{45}=+0.149071198\)
\(a_{46}=-0.258366553\) \(a_{47}=+0.847278905\) \(a_{48}=+0.681107532\) \(a_{49}=-0.175763758\) \(a_{50}=-0.265715430\)
\(a_{51}=+0.170404049\) \(a_{52}=+0.003409285\) \(a_{53}=+1.559270955\) \(a_{54}=+0.255684791\) \(a_{55}=+0.693556828\)
\(a_{56}=-0.283311221\) \(a_{57}=-0.851558762\) \(a_{58}=-2.384731294\) \(a_{59}=+0.036607405\) \(a_{60}=-0.197552421\)
\(a_{61}=+0.030288953\) \(a_{62}=-0.169620283\) \(a_{63}=-0.302624858\) \(a_{64}=-0.488023026\) \(a_{65}=+0.001992739\)
\(a_{66}=+1.189578769\) \(a_{67}=+0.033113503\) \(a_{68}=-0.225823182\) \(a_{69}=-0.112276505\) \(a_{70}=+0.539420726\)
\(a_{71}=+0.449095235\) \(a_{72}=+0.104019957\) \(a_{73}=-0.640826380\) \(a_{74}=+0.361702918\) \(a_{75}=-0.115470054\)
\(a_{76}=+1.128504346\) \(a_{77}=-1.407968398\) \(a_{78}=+0.003417917\) \(a_{79}=-0.536514620\) \(a_{80}=-0.527583625\)
\(a_{81}=+0.111111111\) \(a_{82}=+2.412060990\) \(a_{83}=+0.782556100\) \(a_{84}=+0.401045098\) \(a_{85}=-0.131994409\)
\(a_{86}=-1.724398086\) \(a_{87}=-1.036315623\) \(a_{88}=+0.483954995\) \(a_{89}=+1.247874010\) \(a_{90}=-0.198052588\)
\(a_{91}=-0.004045398\) \(a_{92}=+0.148791287\) \(a_{93}=-0.073710673\) \(a_{94}=-1.125675391\) \(a_{95}=+0.659614581\)
\(a_{96}=-0.724736052\) \(a_{97}=-0.509274820\) \(a_{98}=+0.233515713\) \(a_{99}=+0.516946738\) \(a_{100}=+0.153023448\)

Showing 100 of 150 available coefficients

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